Question: Solve for $x$ and $y$ using elimination. ${-6x-y = -22}$ ${5x-y = 11}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${6x+y = 22}$ $5x-y = 11$ Add the top and bottom equations together. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-6x-y = -22}\thinspace$ to find $y$ ${-6}{(3)}{ - y = -22}$ $-18-y = -22$ $-18{+18} - y = -22{+18}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {5x-y = 11}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - y = 11}$ ${y = 4}$